Question

If the wavelength of a sound source is reduced by a factor of 2, what happens to the waves frequency? What happens to its speed?

Answer 1

The speed $v$, frequency $f$ and wavelength $\lambda$ of a wave are related by the following relation:

$v=f\lambda$

$f=v/\lambda$

now if wavelength is reduced by a factor of 2, ${\lambda }^{\prime }=\lambda /2$

then $f^{\prime }=v/{\lambda }^{\prime }=v/\left(\lambda /2\right)=2\left(v/\lambda \right)=2f$

hence frequency will be doubled .

Now speed of a wave depends upon the medium , as medium is not changed here therefore speed remains constant.